Find the nature of the roots of the quadratic equation $4 x^{2} - 5 x + 3 = 0$ .

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Solution

$4 x^{2} - 5 x + 3 = 0$

Comparing with $a x^{2} + b x + c = 0$ , we get, $a = 4, b = - 5, c = 3$ .

Therefore,
$D = b^{2} - 4 a c = 25 - 4 (4) (3) = 25 - 48 = - 23 < 0$ .

Hence, the given equation has no real roots.

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